How, specifically, have these books helped people? Anyone go from really weak to really strong?
Like many things in life, it depends upon the seriousness of the problem that one has. Using our current understanding about how the mind works can, and does, have a major impact on someone's life if they are wiling to use the principles involved.
Somewhat like understanding the mechanics and necessity for a pre-shot routine when playing pool. All good players have a PSR. They may, or may not, recognize that they have one but a PSR is necessary for long term consistency.
If one's fundamentals are poor then understanding a PSR, its components, methods for development, the roll of practice and the application of the principles used to develop a good PSR can go far in assisting a player to quickly improve their playing ability.
If one developed a good PSR based on their natural ability, experience in other sports, and their own intuitive senses then further understanding of the mechanics of a PSR are probably not needed.
For the most part, many people do not have a good understanding of how the mind works nor do they understand the principles used to modify behavior. That is one reason it requires a PhD in psychology and several years of supervised practice before the principles can be applied to change lives.
Depending upon the problem there are some excellent tools that can be used to improve one's playing ability. However, they will often change your thinking and behavior in other areas of your life as well.
There are a few "tricks" that when understood can be used to fairly quickly contribute to the improvement of many players' ability. Here I am thinking primarily about relaxation, specific tools used to improve concentration, and practice routine principles that all lead to an improvement in one's ability.
Probably some of the best research on specific changes that can be made have been conducted in the areas of "Quiet Eye" principles and in "Old way - New way" training. I have not seen specific studies on the improvement of one's ability to concentrate with regard to pool playing but suspect that a review of the literature would lead to the conclusion that the ability to concentrate can be rapidly improved in many people. Research on relaxation techniques has a long distinguished history and contributes to improvement in many sports, though I know of no specific studies related to playing pool. Research in hypnosis and the many offshoots for enhancing concentration are readily available.